Variables | x1, y0..N z3,4 | $x_1$, $z_{3,4}$ |
Square | x1, z3,4 | $a^2$, $$x^y$, $2^{n-1}$ |
Square Root | 9, x | $\sqrt{9}$, $\sqrt{x}$ |
Logarithm | logx, log2x | $\log{}x$, $\log_{2}x$ |
Limits | limx→∞ | $\lim_{x\to \infty}$ |
Fraction | 21, (−21)n | $\frac{1}{2}$, $\left(-\frac{1}{2}\right)^n$ |
Infinity | ∞ | $infty$ |
Real numbers, Integers, Natural numbers, Rational numbers, Irrational numbers | R, Z, N, Q, P | $\Bbb R$, $\Bbb Z$, $\Bbb N$, $\Bbb Q$, $\Bbb P$ |
Absolute Value | ∣x∣, ∣2x∣, ⌊x⌋, ⌈x⌉ | $\vert{x}\vert$, $\vert\frac{x}{2}\vert$, $\lfloor{x}\rfloor$, $\lceil{x}\rceil$ |
Arithmetic | 4+3, 3−3, 3×3, 3÷3 | $4 + 3$, $3 - 3$, $3\times 3$, $3\div 3$ |
Factorial | n! | $n!$ |
Trigonometric functions | sinθ, cosθ, tanθ | $\sin\theta$, $\cos\theta$, $\tan\theta$ |
Greater or Less | a>b, a≥b, a<b, a≤b | $a\gt b$, $a\geq b$, $a\lt b$, $a\leq b$ |
Much Less Than, Much Greater Than | a≪b, b≫a | $a \ll b$, $b \gg a$ |
Equation | a=b, a=b, a≈b | $a=b$, $a\neq b$, $a\approx b$ |
Times Dot | a⋅b=ab | $a\cdot b=ab$ |
Divide Fraction | a/b=ba | $a/b=\frac{a}{b}$ |
Trinomial Equation | a2+b2=c2 | $a^2 + b^2 = c^2$ |
Matrix Parentheses | (acbd) | $$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ |
Matrix Brackets | [acbd] | $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$ |
Matrix Equation | acbd=ad−bc | $$\begin{vmatrix} a & b \\ c & d \end{vmatrix}=ad-bc$$ |
Set | x∈A, A∋x, x∈/A | $x\in A$, $A\ni x$, $x\notin A$ |
Subset | A⊂B, A⊆B, A⊂B | $A\subset B$, $A\subseteq B$, $A \not \subset B$ |
Intersection & Union | A∩B, A∪B, A | $A\cap B$, $A\cup B$, $\overline{A}$ |
Logical Operators | ∀X,∧X,∨X,¬X,∃A,A⟹B | $$ \forall X, \wedge X, \vee X, \neg X, \exists A A \implies B $$ |
Quadratic Formula | x=2a−b±b2−4ac | $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$ |
Binomial | 3x−1+(1+x)2 | $\sqrt{3x-1}+(1+x)^2$ |
Differentiation | f′, f(n), Dxf | $f'$, $f^{(n)}$, $D_x f$ |
Integral | ∫01f(x)dx | $\int_0^1 f(x) dx$ |
Sigma | i=1∑k | $\displaystyle \sum_{i=1}^k$ |
Integral Large | ∫−∞∞f(x)dx | $\displaystyle \int_{-\infty }^{\infty}f(x)dx$ |
Max Sample | max(a,b)={ab(a≧b)(a<b) | $$\max(a,b)=\begin{cases}a&(a\geqq b)\\b&(a\lt b)\end{cases}$$ |
Piecewise Equations | f(n)={n/2,3n+1,if n is evenif n is odd | $$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}$$ |
Tables | $$\begin{array}{c | lcr} n & \text{Left} & \text{Center} & \text{Right} \ \hline 1 & 0.24 & 1 & 125 \ 2 & -1 & 189 & -8 \ 3 & -20 & 2000 & 1+10i \end{array}$$ |
Set Comprehensions | \{x \text{ if x is even} \mid x^2\in\Bbb Z\} | $\{x \text{ if $x$ is even} \mid x^2\in\Bbb Z\}$ |